SOLUTION: Suppose you have 16 coins that equal at least $2.20. Some coins are quarters and some are nickels. What is the greatest amount of nickels you can have?

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Question 1067268: Suppose you have 16 coins that equal at least $2.20. Some coins are quarters and some are nickels. What is the greatest amount of nickels you can have?
Found 2 solutions by swincher4391, MathTherapy:
Answer by swincher4391(1107) (Show Source):
You can put this solution on YOUR website!
Let n = number of nickels, q = number of quarters.
Then we have n+q =16 and .05n+.25q >= 2.20
Notice that we have two other constraints. 0<=n=<16 and 0<=q<=16
So the solution that gives us exactly 16 coins and exactly 2.20 would be set by
n+q=16 and .05n+.25q=2.20
q=16-n by solving the 1st equation for q.
.05n + .25(16-n) = 2.20
.05n + 4 - .25n = 2.20
.2n = 1.80
n = 9 (so q = 7)
So n is at least 9.
Now, the question is what is the greatest?
We can logically say that for every nickel I add, I have to subtract a quarter (meaning the net amount of money is decreased by 20 cents).
So for instance if n = 10, then q = 6, so we have .5 + 1.50 = 2.00 (which isn't at least 2.20).
Now we can have n=8 and we will go to 2.40, but that's not the "maximum" number of nickels.
So, the maximum number of nickels is 9.
I'll attempt to graph what is going on.

This is using q = 16-n
and q >= 8.8-.2n
Notice that the intersection of the graphs for (n,q) is (9,7)

Answer by MathTherapy(10556) (Show Source):
You can put this solution on YOUR website!
Suppose you have 16 coins that equal at least $2.20. Some coins are quarters and some are nickels. What is the greatest amount of nickels you can have?

Let number of quarters, and nickels be Q and N, respectively
Then we have:

------- Multiplying by 20
------- (1)
Also, we have: Q + N = 16_____Q = 16 - N
------- Substituting 16 - N for Q in (1)
------- Multiplying by LCD, 5

N, or
Therefore, the GREATEST number of nickels is: 9